In my opinion, Men being given the rule of Middle-earth was arguably the right choice. I say arguably because, as the question points out, Men are weak and corruptible by nature. I don't think anyone can refute that, though they could argue it perhaps. But I think that even though this holds true for Man in general... like here, the Men in Middle-earth had heart and perseverance. Men learn from mistakes made, in general, and do their best overall to make things better. Though there are a few in every crowd that are just plain old bad and nothing can be done to turn them from their path, I think on the whole the Men were the right choice because of their ability to adapt and to change to their environments both physically and even politically. Had a race like the Elves been given the rule over Middle-earth it would have been a different place surely. But could anyone say definitively better? I don't think they could. Elves are more wise, more steady, and longer lived than Men, but I also think that because of that they don't take to change very well. Their world is more constant and doesn't do much in the way of deviating from their preferred path. Because of that, I can't say that it would have been better. Just different. Certainly the events of Middle-earth would have been different if any of the other races were to rule it simply because they would have made different choices based on the climate they faced. I can imagine a place that would be a bit closer to Utopia had the Elves ruled, though it may have been a bit more rigid. Had the Dwarves been given the opportunity, I can imagine that there would be a very big economical climate what with their mining of various items like gold and precious gems (Thorin's ancestors come to mind) which would shape the world differently. In the end, however, I think Men were the best choice despite their flaws because of their malleability in terms of change, their ability to learn and grow, and their willingness to defend their world from evils like Malkor and Sauron.

Men have more weaknesses due to being mortal, but I think they were brought to middle earth because even though they are weaker than the other creatures, they are leaders. Men are able to set rules that will be easier for the creatures to follow. They are able to reason and usually talk calmly. They are better able to understand more about how things work in society. That's why I think they were chosen. I think it was the right choice to use men to rule Middle Earth. I can't imagine what would happen if other creatures ruled Middle Earth, a lot of them would cause chaos. It's kind of like, in a way in the Wizards Council, labeling different magical creatures as beast or being. You wouldn't identify a dragon as a being, but as a beast. I can't imagine the trouble that would cause at the ministry meetings if dragons were considered beings, yikes! So I do agree that men are the best to rule Middle Earth. The other creatures in Middle Earth wouldn't have the right skills needed to rule all of Middle Earth.

I actually believe that ‘the gift of men’ made men ideal for ruling Middle Earth. To know you are mortal gives you a different perspective on life: you’re more likely to act and to solve the problem in front of you, rather than to wait to see how things play out (as an elf might, with time to do so). It’s as Siobhan said: because they’re mortal, they’re more willing to respond and adapt to their current situation. This isn’t the case with elves (who are inclined to watch things play out) or Dwarves (who are stubborn and set in their ways).
Also, being mortal is actually a guard against the very qualities that might make men unfit to rule. While they are emotional and corruptible, their rule will always be brief. If someone is a bad ruler, his term is finite and will pass which is not the case with an immortal ruler who might rule as a tyrant for centuries. This gives men a lineage and a history to refer back to. It is far easier to learn from the triumphs and mistakes of other people than it is to be self-reflective enough to learn from your own. It is also something of a guard against tyranny: while corruption might become institutionalised and inherent in a ruling line, sooner or later an individual will break the pattern. That is not the case with longer lived rulers.

"Does the Walker choose the path or the path the walker?" -Garth Nix
(Av/sig by Amy!)